Under your gmail account's settings in Thunderbird, look for '''Manage Identities''' and see if you can add your domain's address there. This would allow you to use it as a "from:" address. However, I'm not sure that gmail won't swap it for the gmail address when you send; this is one of the quirks of gmail. You could add your address as an alias (or "send as" option, or whatever they call it) to the gmail account (you need to go to the gmail website for this), but I suspect you'd need to send and receive a message to authenticate it and this may fall over without it having a password.